Mathematically, which frame has the highest correlation with highest final score, or winning a bowling competition?
How does one factor in the 11th and 12th frames, which are conditional on previous strikes, which obviously pump up the score?
I found this score calculator and tried a few scenarios. Starting from a perfect game, I found out that a failure, no mark or no strike, will give you the exact same score if the miss occurs in frames 3-10. There is no 11th and 12th frame, you simply get extra throws in the 10th frame, so my starting value includes all 3 strikes in the 10th as being part of the 10th.
Failures in the 2nd frame gave a slightly higher score, because the reduced pin count is only added to the strike in the 1st frame, not added to two strikes, like it does in all other frames. A failure in the 1st frame reduces the score least of all, because it doesn’t impact the score of prior strikes.
So, by my calculations, frames 3-10 are equally weighted, and most valuable, frame 2 is slightly less valuable, and frame 1, the least valuable.
As a side note, there are two skills that drive up your score the most. First is making spares, a made spare basically doubles the value of the frame. Second is bunching strikes, a lone strike is hardly worth anything more than a spare, but 2 strikes in a row is worth about 10 pins more than spares, and it goes up 10 pins for each additional strike.
The analysis that frame 1 is least valuable makes sense. Although it would be interesting to see if real statistics back up the claim that frames 3-10 are equally correlated.
I think the 1st is the most valuable. From a score standpoint, if you spare the 1st, you can still bowl 290. Spare the 2nd, and 280 is the max. After that, your best possible score is 270 plus whatever your miss is (i.e. 279 for a 9-spare).
Then again, the 10th can be worth up to 60 depending on your previous shots.
Cheesesteak makes a good point about the 1st and 2nd having the least impact on your score because you’re not screwing up previous marks, though.
Guess it depends on what you consider important, maximizing your scoring, or minimizing your error.
Yes.
I bowled for many, many years. Strikes are nice but spares win games. That means that your first roll in a frame needs to be a strike or a high-count roll that leave a spare that can be made easily.
Well, spares help a lot, but they don’t get you past 200, which is what you get alternating spares and strikes. To get past 200 (usually the mark of a good game), you have to be able to bunch strikes.
The first ball you roll in frames 3 to 10 is guaranteed to have EXACTLY the same scoring impact upon the game. Psychological impact, however, is quite different. In that vein, I always considered the 9th frame the most important frame, because if you didn’t strike the ninth, striking out the tenth was so much less valuable.